The invention relates to signal processing, and more particularly to tone detection in optical systems.
In some detection schemes, a WDM (wavelength-division multiplexed) optical signal carrying a plurality of channels has impressed upon each of its channels a respective unique dither resulting in each channel having a unique tone. Typically, the channels are modulated via amplitude modulation resulting in AM (Amplitude Modulation) tones each having a fixed modulation depth, for example, of approximately 8%. Other modulation schemes are also used. Since the tones have a fixed modulation depth, channel power is a function of the tone power and channel power is measured by detecting the tones of fixed modulation depth. To detect the tones impressed on channels of the WDM optical signal, N time domain samples of the power of the WDM optical signal are collected at a sampling frequency, fs. Typically, a DFT (Discrete Fourier Transform), a radix-M FFT (Fast Fourier Transform) or any other conventional transform is performed upon the N time domain samples to produce N frequency domain samples each having a unique center frequency.
To produce N frequency domain samples from N time domain samples DFTs require a number of arithmetic operations of the order of N2. In comparison, a conventional radix-M FFT requires on the order of NlogM(N) arithmetic operations. FFTs are therefore computationally efficient when compared to DFTs even for N as low as 100. However, a conventional radix-M FFT requires that the N frequency domain samples be computed simultaneously. Generally, only a fraction of the N frequency domain samples contain tones and as such only those frequency domain samples containing tones are required. Therefore since a portion, which can be significant, of the N frequency domain samples calculated are not required, the efficiency of the conventional radix-M FFT is compromised.
Various methods and apparatuses are provided for performing a radix-M FFT (Fast Fourier Transform) upon N time domain samples to produce N/S frequency domain samples for detecting tones of dithers impressed on channels of a WDM (wavelength Division Multiplexed) optical signal. Successive tones have a tone frequency spacing, xcex94fta, and a sampling frequency, fs, is chosen so that fs=Nxcex94fta/S. The sampling frequency, fs, is also less than or equal to a maximum sampling frequency, fs,max, at which the time domain sample can be sampled. Center frequencies of successive frequency domain samples of the N/S frequency domain samples differ by Sxcex94f where S is an integer given by S=Mw with w being an integer and xcex94f=fs/N being a frequency bandwidth. The radix-M FFT is performed in k=logM(N) stages, r, where 1xe2x89xa6rxe2x89xa6k and within each one of the stages, r, radix-M computations are performed on data points that correspond to the N time domain samples prior to the radix-M FFT. More particularly, within a stage, r, where 1xe2x89xa6rxe2x89xa6w, N/Mr radix-M computations are performed and within a stage, r, where w less than rxe2x89xa6k, N/Mw+1 radix-M computations are performed. This results in a reduction in the number of radix-M computations required when compared to a conventional radix-M FFT. The methods and apparatuses may be used to measure channel power. Furthermore, the radix-M FFT may be used to operate on a sequence of 2N real valued time domain samples by re-arranging the 2N real valued time domain samples into a sequence of N complex valued time domain samples, performing the radix-M FFT upon the sequence of N complex valued time domain samples and then applying a split function to recover N/S frequency domain samples.
In accordance with a first broad aspect of the invention, provided is a method of performing a radix-M FFT (Fast Fourier Transform). M is an integer satisfying Mxe2x89xa72. The method involves sampling a signal, containing tones, with a sampling frequency, fs, to produce N time domain samples. Each time domain sample initializes a respective one of N data points, wherein N is an integer. To produce frequency domain samples having a frequency bandwidth xcex94f=fs/N and center frequencies of frequency spacing Mwxcex94f with w being an integer satisfying wxe2x89xa71, in a reduced number for calculation the following steps are performed. For each one of k stages wherein k=logM(N), radix-M computations are performed upon a respective subset of the N data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. Furthermore, the sampling frequency, fs, used is such that the frequency domain samples contain the tones.
In some embodiments of the invention, for a stage, r, of the k stages wherein r is an integer satisfying 1xe2x89xa6rxe2x89xa6w, N/Mr radix-M computations may be performed upon its respective subset of the N data points. Furthermore, for a stage, r, of the k stages wherein w less than rxe2x89xa6k, N/Mw+1 radix-M computations may be performed upon its respective subset of the N data points.
In some cases the tones may have a frequency spacing, xcex94fta, and the sampling frequency, fs, may satisfy fs=Nxcex94fta,/Mw.
The method may be applied to a WDM (Wavelength Division Multiplexed) optical signal having a plurality of channels. Some of the channels may each have impressed upon itself a unique dither resulting in a respective unique tone. The unique tone may have a tone frequency, fta, satisfying fta=axcex94fta+C where a is an integer and C in a positive real number. The unique tones may be detected and then converted into a power.
In accordance with another broad aspect, provided is a method of performing a radix-M FFT where M is an integer satisfying Mxe2x89xa72. The method includes sampling a signal, containing tones, with a sampling frequency, fs, to produce a sequence of 2N real valued time domain samples, wherein N is an integer. The sequence of 2N real valued time domain samples is split into two sequences of N real valued data points and the two sequences of N real valued data points are combined into a sequence of N complex valued data points. To produce frequency domain samples having a frequency bandwidth, xcex94f=fs/N, and center frequencies of frequency spacing Mwxcex94f with w being an integer satisfying wxe2x89xa71, the following steps are followed: 1) for each one of k stages wherein k=logM(N), radix-M computations are performed upon a respective subset of the sequence of N complex valued data points. The respective subset contains only data points upon which the frequency domain samples are dependent; and 2) after the radix-M FFT computations have been performed for each one of the k stages, a split function is applied only to data points of the sequence of N complex valued data points upon which the frequency domain samples are dependent. Furthermore, the sampling frequency, fs, is such that the frequency domain samples contain the tones.
Data points obtained from the split function which correspond to the frequency domain samples may be re-ordered using bit reversal operations.
In accordance with another broad aspect, provided is a processing apparatus which is used to perform a radix-M FFT upon N time domain samples, wherein N and M are integers with Mxe2x89xa72. The N time domain samples are sampled at a sampling frequency, fs, from a signal containing tones to produce frequency domain samples that contain the tones. The apparatus has a memory adapted to store data which include N data points each being initialized by a respective one of the N time domain samples. The apparatus also has a processor capable of accessing the memory. The processor is used to perform, for each one of k stages wherein k=logM(N), radix-M computations upon a respective subset of the N data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. Furthermore, the frequency domain samples have a frequency bandwidth, xcex94f=fs/N, and have center frequencies of frequency spacing Mwxcex94f with w being an integer satisfying wxe2x89xa71 and the sampling frequency, fs, is such that the frequency domain samples contain the tones.
In accordance with another broad aspect, provided is a processing apparatus used to perform a radix-M FFT upon a sequence of 2N real valued time domain samples, wherein N and M are integers with Mxe2x89xa72. The 2N real valued time domain samples are sampled at a sampling frequency, fs, from a signal containing tones to produce frequency domain samples that contain the tones. The apparatus has a memory which is used to store data comprising the sequence of 2N real valued time domain samples. The apparatus also has a processor capable of accessing the memory. The processor is used to split the sequence of 2N real valued time domain samples into two sequences of N real valued data points and combine the two sequences of N real valued data points into a sequence of N complex valued data points. The processor then performs, for each one of k stages wherein k=logM(N), radix-M computations upon a respective subset of the sequence of N complex valued data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. The processor then applies a split function only to data points of the sequence of N complex valued data points upon which the frequency domain samples that contain the tones are dependent. The frequency domain samples have a frequency bandwidth, xcex94f=fs/N, and center frequencies of frequency spacing Mwxcex94f with w being an integer satisfying wxe2x89xa71. Furthermore, the sampling frequency, fs, is such that the frequency domain samples contain the tones.
Data points obtained from the split function which correspond to the frequency domain samples that contain the tones may be re-ordered, using bit reversal operations.
In accordance with another broad aspect, provided is an article of manufacture. The article has a computer usable medium having computer readable program code means embodied therein for causing a radix-M FFT upon a sequence of N time domain samples, wherein N and M are integers with Mxe2x89xa72. The N time domain samples are sampled at a sampling frequency, fs, from a signal containing tones to produce frequency domain samples that contain the tones. The N time domain samples each initialize a respective one of N data points. The computer readable code means in the article of manufacture has computer readable code means for performing, for each one of k stages wherein k=logM(N), radix-M computations upon a respective subset of the N data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. The article has computer readable code means for determining the sampling frequency, fs, so that the frequency domain samples have a frequency bandwidth, xcex94f=fs/N, and have center frequencies of frequency spacing Mwxcex94f with w being an integer satisfying wxe2x89xa71, and so that the frequency domain samples contain the tones.
In accordance with yet another broad aspect, provided is an article of manufacture. The article has a computer usable medium having computer readable program code means embodied therein for causing a radix-M FFT upon a sequence of 2N real valued time domain samples. N and M are integers with Mxe2x89xa72 and the 2N real valued time domain samples are sampled at a sampling frequency, fs, from a signal containing tones to produce frequency domain samples that contain the tones. The computer readable code means in the article of manufacture has computer readable code means for splitting the sequence of 2N real valued time domain samples into two sequences of N real valued data points and combining the two sequences of N real valued data points into a sequence of N complex valued data points. The article has computer readable code means for performing, for each one of k stages wherein k=logM(N), radix-M computations upon a respective subset of the N complex valued data points. The respective subset contains only data points upon which the frequency domain samples that contain the tones are dependent. The article has computer readable code means for applying a split function only to data points of the sequence of N complex valued data points upon which the frequency domain samples are dependent. This is done after the radix-M computations are performed for each one of k stages. The article also has computer readable code means for determining the sampling frequency, fs, so that the frequency domain samples have a frequency bandwidth, xcex94f=fs/N, and have center frequencies of frequency spacing Mwxcex94f with w being an integer satisfying wxe2x89xa71, and so that the frequency domain samples contain the tones.